Abstract
This overview is an introduction to the basic constructive algebraic structures with apartness with special emphasises on a set and semigroup with apartness. The main purpose of this paper, inspired by Bauer [2], is to make some sort of understanding of constructive algebra in Bishop’s style position for those (classical) algebraists as well as for the ones who apply algebraic knowledge who might wonder what is constructive algebra all about. Every effort has been made to produce a reasonably prepared text with such definite need. In the context of basic constructive algebraic structures constructive analogous of isomorphism theorems will be given. Following their development, two points of view on a given subject: classical and constructive will be considered. This overview is not, of course, a comprehensive one.
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